Goodness-of-fit tests for non-Gaussian linear causal models
The field of causal discovery develops model selection methods to infer cause-effect relations among a set of random variables. For this purpose, a number of different modeling assumptions have been proposed that render cause-effect relations identifiable. A prominent example is the assumption that the joint distribution of the observed variables follows a linear non-Gaussian structural equation model. In this talk, we present novel goodness-of-fit tests that assess the validity of this assumption. Our approach is based on testing algebraic relations among second and higher moments that hold as a consequence of the linearity of the structural equations. Specifically, we show that the linearity assumption implies rank constraints on matrices and tensors formed from second and higher moments. For a practical implementation of our goodness-of-fit tests, we consider a multiplier bootstrap method that uses incomplete U-statistics to estimate subdeterminants, as well as asymptotic approximations of the null distribution of singular values. The methods are illustrated, in particular, for the Tübingen collection of benchmark data sets on cause-effect pairs.
Joint with Daniela Schkoda.